Simplify the following expression: $ t = \dfrac{8q}{6q + 8} + \dfrac{8}{5} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{8q}{6q + 8} \times \dfrac{5}{5} = \dfrac{40q}{30q + 40} $ Multiply the second expression by $\dfrac{6q + 8}{6q + 8}$ $ \dfrac{8}{5} \times \dfrac{6q + 8}{6q + 8} = \dfrac{48q + 64}{30q + 40} $ Therefore $ t = \dfrac{40q}{30q + 40} + \dfrac{48q + 64}{30q + 40} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{40q + 48q + 64}{30q + 40} $ $t = \dfrac{88q + 64}{30q + 40}$ Simplify the expression by dividing the numerator and denominator by 2: $t = \dfrac{44q + 32}{15q + 20}$